The present invention relates to the method and resulting cut gemstone of any natural or synthetic refractive material such as diamond, zirconia, ruby, sapphire or emerald of a given refractive index wherein for increased brilliance and depth of color the angles at which the crown (the top half of the stone) and pavilion main facets (the bottom half of the stone) are cut and determined in accordance wit a mathematical formula.
The prior art discloses a number of arrangements for the pavilion and crown main facets including variations of the shape, size and number of each. In all cases it appears that the range of values given for the angle between the crown and pavilion main facets and the plane of the table of the stone were determined by custom or trial and error. No systematic approach to a determination of these angles either for existing gemstone materials or materials yet undiscovered has been explained or explored. Further, no distinction has been drawn between deriving such angles for increased brilliance versus improved depth of color.
Heretofore, no empirical relationship has been used to determine accurately the relationship between the crown and pavilion main facets for a refractive gemstone of a given index of refraction. For examples: U.S. Pat. No. 693,084, Feb. 11, 1902, granted to A. C. Townsend, gives a pattern and position of the facets about the gem but does not demonstrate a way of determining the angles with respect to the axis of the stone. U.S. Pat. No. 2,340,659, Feb. 1, 1944, granted to E. Goldstein gives positions for the facets for improved brilliancy but there is no demonstration of how the angles were determined. Similarly, U.S. Pat. No. 3,286,486, granted Nov. 22, 1966 to James and Harry Huisman discloses an improved arrangement of the pavilion facets including both an increase in the number and improved shape of the facets without giving reasons for the angles. U.S. Pat. No. 3,788,097, granted to Maxims Elbe, Jan. 29, 1974, discloses a range of values for the angle between the pavilion plane and plane of the table of the stone as derived from the prior art methods of cutting, but no explanation is given as to how this range was determined. Instead, the number and configuration of the facets is improved to give increased brilliance and a strong dispersion of colored light or sparkle.
The May 30, 1972 U.S. Patent of Maxims Elbe, 3,665,729, further refines the arrangement of the crown and pavilion facets and the relationship between them but no teaching of how to determine the relationship between the crown and pavilion main facets in different indexes of refraction.
As an illustration of further prior art, the text book, Gem Cutting, A Lapidary Manual, by John Sinkankas (1962) lists a single angle for the pavilion main facets and a range of values for the crown main facets for the known gemstone materials. There is no teaching for the derivation of such angles.
There are two factors which make one transparent gem stone more beautiful than the other - brilliancy and color. All cutting angles are aimed at increasing the brilliancy and creating the exact degree of color desired. Brilliancy is a measure of a stone's ability to return to the eye a maximum amount of the light striking all of the facets above the girdle. Some gemstones are cut for color alone, while light-colored, transparent stones are cut for brilliance as well. Heretofore, depth of color was deepened or lightened by increasing or decreasing the depth of the stone or by decreasing or increasing the angle of the pavilion facets. For example, with tourmaline (dark green) or garnet (deep red), by cutting the pavilion facets shallow, i.e. using lower angles, the stone will be thinner, appearing lighter in color. Similarly light colored stones such as morgamite and kunzite need all the color possible and by increasing the depth of the stone by increasing the pavilion facet angles, the stones gain depth of color.